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## 문제

You are given an matrix of R rows and C columns. All elements of the matrix are by their absolute value smaller than or equal to 104.

You may perform the following operations:

Operation Notation Example
Rotate i-th row of he matrix k elements right rotR i k rotR 3 1
$\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix}\rightarrow \begin{pmatrix} 1&2&3 \\ 4&5&6 \\ 9&7&8\\10&11&12 \end{pmatrix}$
Rotate j-th column of the matrix k elements down rotS j k rotS 3 2
$\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix}\rightarrow \begin{pmatrix} 1&2&9 \\ 4&5&12 \\ 7&8&3\\10&11&6 \end{pmatrix}$
Multiply all elements in the i-th row by -1, if and only if none of them were multiplied before. negR i negR 2
$\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix}\rightarrow \begin{pmatrix} 1 & 2 & 3 \\ -4 & -5 & -6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix}$
Multiply all elements in the j-th column by -1, if and only if none of them were multiplied before. negS j negS 1
$\begin{pmatrix} 1 & 2 & 3 \\ 0&0&0 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix}\rightarrow \begin{pmatrix} -1 & 2 & 3 \\ 0 & 0 & 0\\ -7 & 8 & 9 \\ -10 & 11 & 12 \end{pmatrix}$

Using limited number of these operations, you need to maximize the sum of all the elements of the matrix.

## 입력

The first line of input contains two integers R and C (1 ≤ R, C ≤ 100), number of rows and columns.

The next R lines contain C integers each. All integers are by their absolute value smaller than 104.

## 출력

The first line of output should contain two integers, the maximal sum obtainable and the number of operations used. We shall call this number T. The next T lines should contain any sequence of operations leading to the sum. Each operation should follow the notation defined in the table below. For details look at sample test cases.

• If the obtained sum is not maximal, one of the elements was multiplied more than once or the sequence of operations printed does not lead to the sum, 0 points are awarded.
• Otherwise, the number of points depends on the number of operations used
• For T≤5×R×C, you are awarded 100% of points allocated to that test case
• For T>5×R×C,  you are awarded 0 points for that test case

## 예제 입력 1

3 4
1 -2 5 200
-8 0 -4 -10
11 4 0 100


## 예제 출력 1

345 2
rotS 2 1
negR 2